# Thermodynamic Question (power plant problem)

• gotrilum
In summary, the coal burning electrical power plant can generate up to 53.6 MW of power, but the minimum possible rate of thermal pollution (heat exhausted into the river) is 19 degrees Celsius.
gotrilum
I am wondering if anyone can confirm this answer I got for the following problem;

A coal burning electrical power plant burns at 706 degrees celsius. Heat is exhausted into the river near the power plant; the average river temperature is 19 degrees celsius. What is the minimum possible rate of thermal pollution (heat exhausted into the river) if the station generates 125 MW of electricity?

*First, I found the efficiency to be .7 (1 - 292.15K / 979.15 K). I took .7 and plugged it into the equation Wasted power Pw = Po[(1/η) - 1] = 125E6*[(1/.7) - 1] = 53.6 MW

Another question I have is where does the equation above come from? Someone insisted that I use this equation but I have no ideal from where it is derived.

Thanks

Power generation of the station = ( heat input - heat output) per second.= Qi - Qo
efficiency = n = (Qi -Qo )/Qi
Qi = (Qi - Qo)/n
Qo = Qi - Qi + Qo = (Qi - Qo)/n - ( Qi - Qo) = ( Qi - Qo)[ 1/n - 1]

The best efficiency a set cycle can achieve between two temperatures is the efficiency of the carnot cycle.

If you always think of efficiency as:
what you get / what you pay for.

By this defintion the efficiency of the cycle is:
Work out / Heat In

Work is the difference in heats between the hot and cold reservoirs. and heat in is of the hot reservoir.

So from the efficiency above we put in out Q values

(Qh - Qc)/Qh

Which reduces to:

Qh/Qh - Qc/Qh
=1-(Qc/Qh)

For a reversible cycle such as this we can write the heat transfer as a functuion of temperatre of the reservoir so it becomes:

efficiency = 1-(Tc/Th)

As Lord Kelvin came up with the above relation about reversible cycles, he called the scale the Kelvin scale (how modest of him) so naturally as you have used above the temperatures are in K.

The biggest thing to take from this is how to think of efficiecny in your mind, it really helped me visualise what the right efficieny is. especially for heat pump and refirigiration cycles.

Last edited:

## What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationship between heat, energy, and work. It studies how energy is transferred and transformed within a system, and how these processes affect the behavior of matter. Thermodynamics is essential in understanding the operation of power plants, as it helps engineers design efficient and effective systems for generating electricity.

## How does a power plant work?

A power plant works by converting various forms of energy, such as chemical, nuclear, or thermal energy, into electricity. This is achieved through a series of processes that involve the use of turbines, generators, and other equipment. In a thermal power plant, for example, the heat generated from burning fossil fuels is used to produce steam, which then drives a turbine to generate electricity.

## What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert thermal energy into mechanical work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The Carnot cycle serves as a benchmark for the maximum efficiency that can be achieved in a heat engine, and it is often used as a basis for comparison with real-world power plant processes.

## What is an efficiency of a power plant?

The efficiency of a power plant is a measure of how well it converts the energy input into useful output, in this case, electricity. It is typically expressed as a percentage and is calculated by dividing the energy output by the energy input. The higher the efficiency, the more effectively the power plant is using its resources to generate electricity.

## How can the efficiency of a power plant be improved?

There are several ways to improve the efficiency of a power plant, including using better materials for heat exchangers and turbines, optimizing the combustion process, and implementing waste heat recovery systems. Regular maintenance and upgrades can also help improve efficiency over time. Additionally, advancements in technology and research can lead to more efficient power plant designs in the future.

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